Question

Arata ca 49¹²+7²⁵ este cub

Answer 1

Răspuns: $\red{ \boxed{\bf \big( {7}^{8} \cdot {2}\big)^{3} \implies \: cub \: perfect }}$

Explicație pas cu pas:

$\bf {49}^{12} + {7}^{25} = \big({7}^{2} \big)^{12} + {7}^{25} =$

$\bf {7}^{2 \cdot12} + {7}^{25} = {7}^{24} + {7}^{25} =$

$\bf {7}^{24} \cdot \big({7}^{24 - 24} + {7}^{25 - 24} \big) =$

$\bf {7}^{24} \cdot \big({7}^{0} + {7}^{1} \big) = {7}^{24} \cdot \big(1 + 7 \big) =$

$\bf {7}^{24} \cdot 8 = {7}^{8 \cdot3} \cdot {2}^{3} =$

$\bf {7}^{24} \cdot 8 = \big( {7}^{8} \big)^{3} \cdot {2}^{3} =$

$\red{ \boxed{\bf \big( {7}^{8} \cdot {2}\big)^{3} \implies \: cub \: perfect }}$

==pav38==

Baftă multă !